Adobe Photoshop

Step 1

Open up your image you want to apply the pattern to, I used
the one below.

Step 2

Now we need to make a new document. Make the with and height 3 pixels with a transparent background.
Zoom in using the zoom tool at around 1600% and then grab
the pencil tool and draw 1 black pixel dot in the center like below:

Step 3

Now we need to define the pattern, go to [ Edit > Define Pattern ] and name the pattern dots.

Step 4

Now bring back the image you want to apply the pattern to and select the Fill Bucket Tool.
Look at the top of the screen and select pattern from the fill drop down box and then select the dot pattern from the pattern drop down box.

Step 5

Now make a new layer and fill your image using the Paint Bucket Tool. Play around with various blending options and opacity levels to get the best out of your dots!